Poisson’s Ratio of Thermalized Sheets

The technological revolution of nanostructures has revived the interest in mechanics of atomically thin sheets. In 1980s it was already demonstrated that for freely suspended sheets thermal fluctuations become important beyond the characteristic thermal lengthscale L_th, which is only a few nanometers for graphene at room temperature. It was found that in sheets larger than L_th, elastic constants become scale dependent with universal power law exponents. In many applications, it is important to understand how sheets respond to external forces. In this talk we will focus on the response of sheets to uniaxial tension and in particular to the Poisson’s ratio defined as the negative ratio between the lateral expansion and the expansion in direction of applied load. We employ renormalization group procedure to study the response of sheets in a broad range of applied tensions. For sheets that are much larger than L_th we observe three different regimes. In the linear regime, a universal negative Poisson’s ratio -1/3 is observed, while the intrinsic material constant is recovered for large loads. We find also an interesting intermediate regime, where sheets expand nonlinearly with the universal exponent of ~0.7, which is reminiscent of the critical phenomena in ferromagnetism.